Question:
An electromagnetic wave of intensity 50 Wm\(^{-2}\) enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:
An electromagnetic wave of intensity 50 Wm\(^{-2}\) enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:
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With no loss the intensity stays the same. Use \(I = \frac{1}{2}\varepsilon v E_0^2\) with \(\varepsilon = n^2\varepsilon_0\), \(v=c/n\), and \(B_0 = E_0/v\).
Updated On: Nov 5, 2026
- \(\left(\frac{1}{\sqrt{n}}, \frac{1}{\sqrt{n}}\right)\)
- \(\left(\sqrt{n}, \sqrt{n}\right)\)
- \(\left(\sqrt{n}, \frac{1}{\sqrt{n}}\right)\)
- \(\left(\frac{1}{\sqrt{n}}, \sqrt{n}\right)\)
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The Correct Option is C
Solution and Explanation
Intensity is unchanged: \(I = \frac{1}{2}\varepsilon_0 c E_1^2\) in vacuum and \(I = \frac{1}{2}\varepsilon v E_2^2\) in the medium, where \(\varepsilon = n^2\varepsilon_0\) (non-magnetic medium) and \(v = c/n\).
So \(\varepsilon v = n^2\varepsilon_0\cdot\frac{c}{n} = n\varepsilon_0 c\).
Equate: \(\varepsilon_0 c E_1^2 = n\varepsilon_0 c E_2^2\) so \(\frac{E_1}{E_2} = \sqrt{n}\).
Magnetic field: \(B = E/v\). Before: \(B_1 = E_1/c\). After: \(B_2 = E_2 n/c\).
\(\frac{B_1}{B_2} = \frac{E_1}{nE_2} = \frac{\sqrt{n}}{n} = \frac{1}{\sqrt{n}}\).
Ratios (before : after) are \(\left(\sqrt{n}, \frac{1}{\sqrt{n}}\right)\).
Answer: (3) \(\left(\sqrt{n}, \frac{1}{\sqrt{n}}\right)\)
So \(\varepsilon v = n^2\varepsilon_0\cdot\frac{c}{n} = n\varepsilon_0 c\).
Equate: \(\varepsilon_0 c E_1^2 = n\varepsilon_0 c E_2^2\) so \(\frac{E_1}{E_2} = \sqrt{n}\).
Magnetic field: \(B = E/v\). Before: \(B_1 = E_1/c\). After: \(B_2 = E_2 n/c\).
\(\frac{B_1}{B_2} = \frac{E_1}{nE_2} = \frac{\sqrt{n}}{n} = \frac{1}{\sqrt{n}}\).
Ratios (before : after) are \(\left(\sqrt{n}, \frac{1}{\sqrt{n}}\right)\).
Answer: (3) \(\left(\sqrt{n}, \frac{1}{\sqrt{n}}\right)\)
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